THE DOMAIN OF DEPENDENCE INEQUALITY AND INITIALBOUNDARY VALUE PROBLEMS FOR SYMMETRIC HYPERBOLIC SYSTEMS

Abstract

The usual systems of partial differential equations that govern wave propagation (equations of acoustics, electromagnetics, magnetohydrodynamics, elasticity, etc.) have an energy integral and corresponding Poynting vector which describes the flow of energy. The most general systems of this type were introduced by K. O. Friedrichs, who called them 'symmetric hyperbolic' systems. An a priori domain of dependence inequality is proved for solutions of such systems in cylindrical space-time domains subject to local, dissipative boundary conditions. The inequality expresses the fact that energy propagates with a finite speed in such systems. It is used to derive existence, uniqueness and regularity theorems for solutions of initialboundary value problems for symmetric hyperbolic systems. These problems provide a mathematical model for the diffraction by obstacles of the waves described by such systems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1962
Accession Number
AD0288006

Entities

People

  • Calvin H. Wilcox

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustics
  • Boundaries
  • Differential Equations
  • Diffraction
  • Elastic Properties
  • Electromagnetic Wave Propagation
  • Equations
  • Inequalities
  • Integrals
  • Magnetohydrodynamics
  • Mathematical Models
  • Mathematics
  • Models
  • Partial Differential Equations
  • Time Domain
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space